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Analysis of single-cell transcriptomics often relies on clustering cells and then performing differential gene expression (DGE) to identify genes that vary between these clusters. These discrete analyses successfully determine cell types and markers; however, continuous variation within and between cell types may not be detected. We propose three topologically motivated mathematical methods for unsupervised feature selection that consider discrete and continuous transcriptional patterns on an equal footing across multiple scales simultaneously. Eigenscores (eigi) rank signals or genes based on their correspondence to low-frequency intrinsic patterning in the data using the spectral decomposition of the Laplacian graph. The multiscale Laplacian score (MLS) is an unsupervised method for locating relevant scales in data and selecting the genes that are coherently expressed at these respective scales. The persistent Rayleigh quotient (PRQ) takes data equipped with a filtration, allowing the separation of genes with different roles in a bifurcation process (e.g., pseudo-time). We demonstrate the utility of these techniques by applying them to published single-cell transcriptomics data sets. The methods validate previously identified genes and detect additional biologically meaningful genes with coherent expression patterns. By studying the interaction between gene signals and the geometry of the underlying space, the three methods give multidimensional rankings of the genes and visualisation of relationships between them.

Pseudomonas aeruginosa (P.a) is one of the most critical antibiotic resistant bacteria in the world and is the most prevalent pathogen in cystic fibrosis (CF), causing chronic lung infections that are considered one of the major causes of mortality in CF patients. Although several studies have contributed to understanding P.a within-host adaptive evolution at a genomic level, it is still difficult to establish direct relationships between the observed mutations, expression of clinically relevant phenotypes, and clinical outcomes. Here, we performed a comparative untargeted LC/HRMS-based metabolomics analysis of sequential isolates from chronically infected CF patients to obtain a functional view of P.a adaptation. Metabolic profiles were integrated with expression of bacterial phenotypes and clinical measurements following multiscale analysis methods. Our results highlighted significant associations between P.a “metabotypes”, expression of antibiotic resistance and virulence phenotypes, and frequency of clinical exacerbations, thus identifying promising biomarkers and therapeutic targets for difficult-to-treat P.a infections